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The Riemann–Roch Theorem on higher dimensional complex noncommutative tori

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Abstract We prove analogues of the Riemann–Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how… Click to show full abstract

Abstract We prove analogues of the Riemann–Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how to distinguish “noncommutative abelian varieties” from “non-algebraic” noncommutative complex tori.

Keywords: riemann roch; noncommutative tori; theorem; roch theorem; theorem higher

Journal Title: Journal of Geometry and Physics
Year Published: 2020

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